how can I store values generated from a nested loop into an arrray ?

if I have this code :-

function S = triangle_wave(n) 
  S = zeros(1,1001); %preallocation 
  e = [];
  for t = 0:((4*pi)/1000):(4*pi)
    for k = 0:n
      sigma = (((-1)^k)*sin((2*k+1)*t))/((2*k+1))^2;
      e(1, *???*) = sigma;   *(%what should I put here instead of (???)?)*
    end
    r = sum(e(:));
    S(1, *???*) = r;           *(%what should I put here instead of (???)?)*
  end
end

I can't depend on the loop's variable because they are kinda of rational numbers, so how should i store ?

Answer 1

[Andrei Bobrov]

function S = triangle_wave(n) 
    t = linspace(0,4*pi,1001)';
    k = 0:n;
    S = sum(bsxfun(@times,sin(bsxfun(@times,t,(2*k+1))),(-1).^k./(2*k+1).^2),2);
end

or with for..end loop

function S = triangle_wave(n) 
    S = zeros(1001,1); %preallocation 
    t = linspace(0,4*pi,1001);%0:((4*pi)/1000):(4*pi);
    k = 0:n;
    for jj = 1:1001
        S(jj) = sum(((-1).^k).*sin((2*k+1)*t(jj))./(2*k+1).^2);
    end
end

[Omar Maklad]

Thanks a lot, it works.

Answer 2

[dpb]

Create independent index variables and increment them each pass thru the loop...

"The Matlab way" would be to use the vectorization features in Matlab syntax (see the "dot" operators .* and .^ and friends...)

BTW, if you have Signal Processing Toolbox there are a couple of waveform generation functions there; specifically sawtooth does symmetric triangle-wave form. Unless, of course, the "feature" of the rounded form of the lower number of series in the approximation is an intended result.

Answer 3

[Thorsten]

The general scheme is to do define a vector of values

 t = linspace(tmin, tmax, Nvalues);

and run a loop

 for i=1:numel(t)

   res(i) = your formula depending on t(i)

 end

Of course it is often mor efficient to use vectorisation, as shown in Andrei's answer.